The nitrogen-vacancy center (N-V center or NV center) is one of numerous photoluminescent point defects in diamond. It consists of a nearest-neighbor pair of a nitrogen atom, which substitutes for a carbon atom, and a lattice vacancy.

The most explored and useful properties of an NV center include its spin-dependent photoluminescence (which enables measurement of the electronic spin state using optically detected magnetic resonance), and its relatively long spin coherence at room temperature, lasting up to milliseconds. The NV center energy levels are modified by magnetic fields, electric fields, temperature, and strain, which allow it to serve as a sensor of a variety of physical phenomena. Its atomic size and spin properties can form the basis for useful quantum sensors.

NV centers enable nanoscale measurements of magnetic and electric fields, temperature, and mechanical strain with improved precision. Beyond sensing, NV centers have been investigated as room-temperature polarization sources for nuclear spins in diamond. Optically induced cross relaxation between NV centers and substitutional nitrogen defects (P1 centers) in the ground state has been identified as the dominant mechanism for bulk 13C hyperpolarization, enabling significant enhancement of nuclear magnetic resonance signals without requiring microwave excitation or cryogenic conditions. External perturbation sensitivity makes NV centers ideal for applications in biomedicine—such as single-molecule imaging and cellular process modeling. NV centers can also be initialized as qubits and enable the implementation of quantum algorithms and networks. It has also been explored for applications in quantum computing (e.g. for entanglement generation), quantum simulation, and spintronics.

Production

Natural NV centers are randomly oriented within a diamond crystal. Ion implantation techniques can enable their artificial creation in predetermined positions, as follows.

Nitrogen-vacancy centers are typically produced from single substitutional nitrogen centers (called C or P1 centers in diamond literature) by irradiation followed by annealing at temperatures above 700 °C. A wide range of high-energy particles is suitable for such irradiation, including electrons, protons, neutrons, ions, and gamma photons. Irradiation produces lattice vacancies, which are a part of NV centers. Those vacancies are immobile at room temperature, and annealing is required to move them. Single substitutional nitrogen produces strain in the diamond lattice; it therefore efficiently captures moving vacancies, producing the NV centers.

During chemical vapor deposition of diamond, a small fraction of single substitutional nitrogen impurity (typically <0.5%) traps vacancies generated as a result of the plasma synthesis. Such nitrogen-vacancy centers are preferentially aligned to the growth direction. Delta doping of nitrogen during CVD growth can be used to create two-dimensional ensembles of NV centers near the diamond surface for enhanced sensing or simulation.

Diamond is notorious for having a relatively large lattice strain. Strain splits and shifts optical transitions from individual centers resulting in broad lines in the ensembles of centers. Special care is taken to produce extremely sharp NV lines (line width ~10 MHz) required for most experiments: high-quality, natural (type IIa) diamonds are selected, although synthetic diamonds are preferential. Many of them already have sufficient concentrations of grown-in NV centers and are suitable for applications. If not, they are irradiated by high-energy particles and annealed. Selection of a certain irradiation dose allows tuning the concentration of produced NV centers such that individual NV centers are separated by micrometre-large distances. Then, individual NV centers can be studied with standard optical microscopes or, better, near-field scanning optical microscopes having sub-micrometre resolution.

Structure

The nitrogen-vacancy center is a point defect in the diamond lattice. It consists of a nearest-neighbor pair of a nitrogen atom, which substitutes for a carbon atom, and a lattice vacancy.

Two charge states of this defect, neutral NV0 and negative NV−, exist. The NV0 centers can be converted into NV− by changing the Fermi level position with an external voltage (see ).

On the one hand, the neutral state is not generally used for quantum technology. The NV− state is commonly, and somewhat incorrectly, called "the nitrogen-vacancy center". On the other hand, the modern, detailed structural understanding of the system originates from theoretical considerations and recent electron resonance (EPR) and optically detected magnetic resonance (ODMR) studies on the paramagnetic NV0 state.Several theoretical works have also attempted to treat the system as a molecule and build molecular orbitals using the Linear Combination of Atomic Orbitals (LCAO) approach. Other spectroscopies used to describe the system's general structure include optical absorption and photoluminescence (PL).

In the neutral NV0, the nitrogen atom has five valence electrons. Three are covalently bonded to adjacent lattice carbon atoms, while the other two remain a non-bonded lone pair.

The vacancy carries three valence electrons. Two of them form a quasi covalent bond and one remains unpaired. The overall symmetry, however, is axial (trigonal C3V); one can visualize this by imagining the three unpaired vacancy electrons continuously exchanging their roles in a quantum superposition.

In the negative charge state NV−, an extra electron is located at the vacancy site forming a spin S=1 pair with one of the vacancy electrons. Thus there are 6 electrons in total within the NV− center: 3 from the vacancy, 2 from the nitrogen atom, and 1 extra giving it negative charge. This extra electron induces spin triplet ground states of the form |3A⟩ and excited states of the form |3E⟩. There is an additional metastable state that exists between these spin triplets, that often manifests as a singlet. As in NV0, the vacancy electrons preserve the overall trigonal symmetry.

Energy levels A NV center has a ground-state triplet (3A), an excited-state triplet (3E) and two intermediate-state singlets (1A and 1E). Both 3A and 3E contain ms = ±1 spin states, in which the two electron spins are aligned (either up, such that ms = +1 or down, such that ms = -1), and an ms = 0 spin state where the electron spins are antiparallel. Due to the magnetic interaction, the energy of the ms = ±1 states is higher than that of the ms = 0 state. 1A and 1E only contain a spin state singlet each with ms = 0.Group theory results are used to take into account the symmetry of the diamond crystal, and so the symmetry of the NV itself. Followingly, the energy levels are labeled according to group theory, and in particular are labelled after the irreducible representations of the C3V symmetry group of the defect center, A1, A2, and E. The "3" in 3A2 and 3E as well as the "1" in 1A1 and 1E represent the number of allowable ms spin states, or the spin multiplicity, which range from –S to S for a total of 2S+1 possible states. If S = 1, ms can be −1, 0, or 1.

As discussed below, many properties of the environment affect the precise energy levels and population of the system states:

Amplitude and orientation of a static magnetic field splits the ms = ±1 levels in the ground and excited states. Amplitude and orientation of elastic (strain) or electric fields have a much smaller but also more complex effects on the different levels. Continuous-wave microwave radiation (applied in resonance with the transition between ms = 0 and (one of the) ms = ±1 states) changes the population of the sublevels within the ground and excited state. A tunable laser can selectively excite certain sublevels of the ground and excited states. Surrounding spins and spin–orbit interaction will modulate the magnetic field experienced by the NV center. Temperature and pressure affect different parts of the spectrum including the shift between ground and excited states.

Electromagnetic coupling The Hamiltonian dynamics of a NV center are approximated extremely well by the following sum of interactions with the electromagnetic field:

Each term in the Hamiltonian can be measured under the right conditions.

Optical properties

NV centers emit bright red light (3E→3A transitions), if excited off-resonantly by visible green light (3A →3E transitions). This can be done with convenient light sources such as argon or krypton lasers, frequency doubled Nd:YAG lasers, dye lasers, or He-Ne lasers. Excitation can also be achieved at energies below that of zero phonon emission.

The radiative lifetime of the 3E excited state is around 10 ns in NV- and approximately 20 ns in NV0. At room temperature the NV center's optical spectrum exhibits no sharp peaks due to thermal broadening. However, cooling the NV centers with liquid nitrogen or liquid helium dramatically narrows the lines down to a width of a few MHz. At low temperature it also becomes possible to specifically address the zero-phonon line (ZPL).

An important property of the luminescence from individual NV centers is its high temporal stability. Whereas many single-molecular emitters bleach (i.e. change their charge state and become dark) after emission of 106–108 photons, bleaching is unlikely for NV centers at room temperature. Strong laser illumination, however, may also convert some NV− into NV0 centers.

Because of these properties, the ideal technique to address the NV centers is confocal microscopy, both at room temperature and at low temperature.

State manipulation Temperature and pressure directly influence the zero-field term of the NV center leading to a shift between the ground and excited state levels.

Radiative and non-radiative transitions Optical transitions must preserve the total spin and occur only between levels of the same total spin. Specifically, transitions between the ground and excited states (with equal spin) can be induced using a green laser with a wavelength of 546 nm. Transitions 3E→1A and 1E→3A are non-radiative, while 1A →1E has both a non-radiative and infrared decay path.

The non-radiative transition between 3E and 1A is stronger for ms = ±1 and weaker for ms = 0. This asymmetry enables optical spin-polarization, which initializes the quantum state of a qubit for quantum information processing or quantum sensing. To understand the process, first consider an off-resonance excitation which has a higher frequency (typically 2.32 eV (532 nm)) than all transitions and thus couples to each transition through vibron excitation. A pulse of this wavelength will excite all spin states to 3E. Because the transition to 1A is weak for ms = 0, the spin-zero states radiate back to 3A. But states with ms = ±1 often decay nonradiatively to 1A, at which point the system is in a ms = 0 state. Further decay from 1A tends to preserve ms = 0, and after many cycles the system is in the ms = 0 ground state with high probability.

Static external fields

Microwave irradiation The energy difference between the ms = 0 and ms = ±1 states corresponds to the microwave regime. Population can be transferred between the states by applying a resonant magnetic field perpendicular to the defect axis. Numerous dynamic effects (spin echo, Rabi oscillations, etc.) can be exploited by applying a carefully designed sequence of microwave pulses. Such protocols are rather important for the practical realization of quantum computers. By manipulating the population, it is possible to shift the NV center into a more sensitive or stable state. Its own resulting fluctuating fields may also be used to influence the surrounding nuclei or protect the NV center itself from noise. This is typically done using a wire loop (microwave antenna) which creates an oscillating magnetic field.

Locally constant fields